Proportion Manual Growing Knowing com 2011 1 Sample

Sample proportions �Standard error for proportion = �z score = �ps is sample proportion.

Common error �Take care not to confuse the population proportion p with the sample

�Go to website, do sample proportion problems. Growing. Knowing. com © 2011 6

Confidence using Proportion Growing. Knowing. com © 2011 7

Proportion �We have shown Confidence Levels for Means �We also have Confidence Levels for

Test yourself � Growing. Knowing. com © 2011 9

Practice �Go to website and practice Confidence Interval �Difficulty level 1 and 2 Growing.

Sample size with proportion Growing. Knowing. com © 2011 13

. �You are studying the proportion of students who believe in a soul? What

�Go to website and practice sample size calculations Growing. Knowing. com © 2011 15

Hypothesis Proportion Growing. Knowing. com © 2011 16

Hypothesis Proportion �We have shown hypothesis testing of means, but you can do hypothesis

Formulas for proportion � Growing. Knowing. com © 2011 18

�The claim is that 0. 31 clients respond to sale items, and you want

�Go to website, do hypothesis proportion questions Growing. Knowing. com © 2011 22

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Sample proportions �Standard error for proportion = �z score = �ps is sample proportion. �p is population proportion. �σp is standard error �n is the sample size. �To qualify to use the formula: np ≥ 5 and n(1 -p) ≥ 5 Growing. Knowing. com © 2011 2

Common error �Take care not to confuse the population proportion p with the sample proportion ps �If one is labeled as population or sample, then you know both �If p is given, then the other proportion must be ps and visa-versa �If population and sample are not labelled, then the proportion that is assumed to be true is the p and the value you are testing against is ps Growing. Knowing. com © 2011 5

Proportion �We have shown Confidence Levels for Means �We also have Confidence Levels for Proportion �For proportion, the alpha, confidence levels, margin of error, and interval calculations are the same as Means. �The standard error for proportion uses a different formula than standard error for means. Growing. Knowing. com © 2011 8

. �You are studying the proportion of students who believe in a soul? What should Sample Size be if confidence level = 0. 8, sample proportion = 0. 46, and error rate = 0. 11 ? �Formula = �z = (confidence + alpha/2 = (. 80 +. 2/2 ) =. 9000 Lookup. 9000, z = 1. 28 �n = 0. 46(1 − 0. 46)(1. 28/0. 11)2 = 0. 2484 × 11. 636363642 = 33. 63 � Round up to 34 Growing. Knowing. com © 2013 14

Hypothesis Proportion �We have shown hypothesis testing of means, but you can do hypothesis testing with proportions as well. �We still use the 5 steps of hypothesis testing �Stating the hypothesis, the decision rule, and rejecting the null hypothesis do not change from Hypothesis Testing for Means �What changes is we use proportion formulas from confidence testing and proportion sampling. Growing. Knowing. com © 2011 17

�The claim is that 0. 31 clients respond to sale items, and you want to prove it is less. Your survey of 182 clients showed 32 respond. Test the hypothesis at a 5 % level of significance. �Qualify � Recall that to qualify to use our standard error calculation that np ≥ 5 and n(1 -p) ≥ 5 � 182(. 31) = 56. 42 and n(1 -p) = 125. 58 � Both are over 5, so we qualify. � �There are two ways we may be given proportion data � Given the proportion directly, for example 31% respond, or � For example, 32 out of 182 respond, so we calculate proportion as 32/182 =. 1758 so 17. 58% respond. Growing. Knowing. com © 2011 19